Roman Stepanyan

Concentration fluctuations in polymer solutions under extensional flow

In this work, we extend the classical analysis of concentration fluctuations in polymer solutions under shear flow to consider the same phenomenology under extensional flow. Experimental work by van Egmond and Fuller [Macromolecules 26, 7182–7188 (1993)] revealed a four-lobe scattering pattern for a polystyrene solution in a planar extensional flow field. Similar to earlier results found in shear, they find the existence of finite-wavelength peak intensity locations. To investigate this phenomenon, we couple stress and concentration using a two-fluid model with fluctuations driven by thermal noise incorporated through a canonical Langevin approach. The polymer stress is governed by the Rolie–Poly model augmented with finite extensibility to account for large stretching of chains at high Weissenberg numbers. Perturbing the equations about homogeneous planar extensional flow for weak amplitude inhomogeneities, but arbitrary flow strength, we solve for the steady correlations. The resulting structure factor ...

A simple constitutive model for a polymer flow near a polymer-grafted wall

A simple constitutive model is proposed to describe a polymer flow near a polymer-grafted wall. The model is based on a generalization of the Rolie-Poly equation [A. E. Likhtman and R. S. Graham, J. Non-Newton. Fluid Mech. 114, 1–12 (2003)] to a “bulk+wall” system combined with a microscopic picture of the relaxation of the tethered chains. Different grafting regimes are considered, varying from nonoverlapping to strongly interacting tethered chains. Despite its simplicity, the model allows one to reproduce all the generic features of the flow. Different scaling regimes are predicted, in accord with earlier studies, and the transition between them is quantified. Special attention is paid to a careful comparison to available experimental data: a reasonable agreement is demonstrated and possible shortcomings of the model are discussed.